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Simplify the expression:

[tex]\[

(2x^5 - 7x^3 + x^2 - 4) - (5x^4 + 4x^2 + 3)

\][/tex]

A. [tex]\(-3x^5 - 7x^3 - 3x^2 - 7\)[/tex]

B. [tex]\(7x^5 - 7x^3 + 5x^2 - 1\)[/tex]

C. [tex]\(2x^5 + 5x^4 - 7x^3 + 5x^2 - 1\)[/tex]

D. [tex]\(2x^5 - 5x^4 - 7x^3 - 3x^2 - 7\)[/tex]

Answer :

We start with the expression

[tex]$$
\left(2x^5 - 7x^3 + x^2 - 4\right) - \left(5x^4 + 4x^2 + 3\right).
$$[/tex]

Step 1. Distribute the subtraction over the second polynomial:

[tex]$$
2x^5 - 7x^3 + x^2 - 4 - 5x^4 - 4x^2 - 3.
$$[/tex]

Step 2. Rearrange the terms in descending order of powers:

[tex]$$
2x^5 - 5x^4 - 7x^3 + x^2 - 4x^2 - 4 - 3.
$$[/tex]

Step 3. Combine like terms:

- For the [tex]$x^2$[/tex] terms:
[tex]$$
x^2 - 4x^2 = -3x^2.
$$[/tex]
- For the constant terms:
[tex]$$
-4 - 3 = -7.
$$[/tex]

Thus, the expression simplifies to

[tex]$$
2x^5 - 5x^4 - 7x^3 - 3x^2 - 7.
$$[/tex]

This corresponds to option D:

[tex]$$
2x^5 - 5x^4 - 7x^3 - 3x^2 - 7.
$$[/tex]

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